• Title, Summary, Keyword: 수치해

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Numerical Solution of an Elliptic Type H-J-B Equation Arising from Stochastic Optimal Control Problem (확률 최적 제어문제에서 발생되는 Elliptic Type H-J-B 방정식의 수치해)

  • Wan Sik Choi
    • Journal of Institute of Control, Robotics and Systems
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    • v.4 no.6
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    • pp.703-706
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    • 1998
  • 본 논문에서는 확률 최적 제어문제에서 발생되는 Elliptic type H-J-B(Hamilton-Jacobi-Bellman) 방정식에 대한 수치해를 구하였다. 수치해를 구하기 위하여 Contraction 사상 및 유한차분법을 이용하였으며, 시스템은 It/sub ∧/ 형태의 Stochastic 방정식으로 취하였다. 수치해는 수학적인 테스트 케이스를 설정하여 검증하였으며, 최적제어 Map을 방정식의 해를 구하면서 동시에 구하였다.

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Finite Element Simulation of High-Speed Impact in Plane Structure (고속충격하중을 받는 평면구조의 유한요소해석)

  • 황갑운
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.12 no.2
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    • pp.119-128
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    • 1999
  • 본 연구는 등방탄성체에 고속충격하중이 작용하는 경우에 대한 유한요소해석에 관한 것으로 대상구조는 여러 가지 모양의 2차원 평면구조를 택하였다. Galerkin 방법을 이용하여 유한요소 정식화하였으며 직접시간적분법에 의해 수치해를 구하였다. 본 해석에서는 균열이 없는 평판으로 수치해와 이론해를 비교하여 수치해의 신뢰성을 확인하였으며, 0°, 30°, 45°경사 균열이 없는 평판에 적용한 3가지 예를 분석하였다. 수치해석 결과는 이론해의 결과와 상호 잘 일치하였다.

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A Comparison of Low-Dimensional Reactor Kinetics Analysis Methods with Modified Borresen's Coarse-Mesh Method (저차원 원자로 동특성 해법과 다차원 수정형 Borresen 소격해법의 비교)

  • Kim, Chang-Hyo;Lee, Gyu-Bok
    • Nuclear Engineering and Technology
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    • v.22 no.4
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    • pp.359-370
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    • 1990
  • This study concerns with comparing low-dimensional reactor kinetics methods with a three-dimensional kinetics method to be used for safety analysis of light water reactors in order to suggest means of preparing input parameters required for low-dimensional methods. For this purpose a one-dimensional finite difference two-group diffusion theory code ODTRAN and a third-order Hermit polynomial-based point kinetics code POTRAN are developed and used to obtain low-dimensional solutions to the LRA-BWR kinetics benchmark problem. The results are compared with a three-dimensional modified Borresen's coarse-mesh solution of the kinetics problem by CMSNACK code. Through this comparison some simple but practical means of preparing input parameters of low-dimensional kinetics analysis methods are suggested.

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Finite Element Solution of Helmholtz Equation for Free Harbor Oscillation (항만 고유 진동 해석을 위한 Helmholtz 방정식의 유한요소 해법)

  • Ryu, Yeon Sun;Lee, Byung Gul
    • Journal of The Korean Society of Civil Engineers
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    • v.13 no.1
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    • pp.47-54
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    • 1993
  • For the numerical analysis of free oscillation characteristics in a harbor with general boundary and bottom topography, finite element method is applied. The governing Helmholtz equation is transformed into a generalized matrix eigenvalue problem using the standard finite element procedure. A computer code is developed for the numerical evaluation of natural frequencies and free oscillation modes. In the eigensolution process, a shifting strategy is devised for the treatment of numerical singularity. Scaling of coefficient matrix is also found to be effective for the alleviation of numerical ill-conditioning. For the test problems, firstly, analytical and numerical solutions are compared and validity of the code is obtained. Hence the method is successfully applicable for the real-world problems with general geometric boundaries and bottom topography.

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An Analytical Solution of One Dimensional Mild Slope Equation by the WKB method (WKB 방법에 의한 일차원 완경사 파랑식의 해석해)

  • Seo, Seung-Nam
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.20 no.5
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    • pp.461-471
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    • 2008
  • An analytical solution of one dimensional mild slope equation is derived by use of the WKB method, which has a form similar to Porter's solution(2003). The present solution is so general in the sense of application that it is comparable to the corresponding numerical solutions. In the derivation we also presented the solution of refraction equation in terms of surface displacement. Some numerical results of the present solution by use of Bremmer's method are presented which agree with existing numerical solutions.

Analysis and Simulation of Ultrasonic Wave Propagation and Scattering in Unidirectional Fiber Composites (단일방향 섬유 복합재료 내의 초음파 전파 및 산란 현상의 해석과 시뮬레이션)

  • Lee, Choon-Jae;Yim, Hyun-June
    • Journal of the Korean Society for Nondestructive Testing
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    • v.21 no.3
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    • pp.269-276
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    • 2001
  • Ultrasonic testing of composite materials is much more difficult than that of isotropic materials, because of the beam skew phenomenon caused by their elastic anisotropy. An established analytical method exists for elastic wave propagation in anisotropic media as a result of previous research efforts. Yet, due to the complexity of the analytical method, solution of real problems must resort to the numerical method. In this work, analytical solutions have first been obtained for the wavefield due to a point source in a unidirectional fiber-reinforced composite, which may be modeled as transversely isotropic. Then, the corresponding numerical solutions have been obtained using the mass-spring lattice model(MSLM). The two solutions have agreed well with each other. Other problems such as reflection from free boundaries and scattering from cracks have also been solved numerically, and the results have been investigated from the viewpoint of wave mechanics. The numerical model whose validity has been confirmed by this work will be of great use in simulating ultrasonic testing of composite materials.

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Papers : Analysis of Numerical Instability of AUSM - type Schemes (논문 : AUSM 계열 수치기법의 수치적 불안정성에 대한 분석)

  • Kim,Gyu-Hong;Lee,Gyeong-Tae;Kim,Jong-Am;No,O-Hyeon
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.30 no.3
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    • pp.27-36
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    • 2002
  • Numerical stability is studied based on numerics and mathematics. It is frequently observed in the region where velocity is zero. In that region, the Euler equation have numerous solutions and, thus, it is impossible to determine a unique solution with only governing equations. However, a unique solution can be determined by additional outer flow conditions or outer numerical discontinuity calculation since the information or a unique solution under undisturbed conditions is lost by disturbances. In this reason, the numerical scheme comsistent with Euler equations cannot remove shock instability completely.

Finite Difference Numerical Solutions for Isotropic Rectangular Thin Elastic Plates with Three Edges Clamped and the Other Free (등방성 직사각형의 3변 고정 1변 자유 얇은 탄성판에 대한 유한차분법의 수치해)

  • Seo Seung-Nam
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.18 no.3
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    • pp.225-240
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    • 2006
  • In order to calculate bending moments of rectangular plates with three edges clamped the other free subjected to both a uniform load and a triangular load, a finite difference equation for the non-dimensional governing equation are presented and numerical solutions with different aspect ratios and/or number of grid points are analyzed. The finite difference solutions are obtained by use of grid points up to 11,520 and the optimum grid points according to aspect ratios of the plate are presented as well. The obtained numerical solutions are shown to satisfy the given x moment boundary condition at the free edge, which can not be satisfied in Levy's analytical solutions and peculiar behaviour of the calculated moments is observed around the corners between the free edge and fixed ones. The numerical solutions of bending moments subjected to both a uniform load and a triangular load are compared with the corresponding analytical solutions which are shown in very good agreement on the solution domain except the neighborhood of the free edge.

Sensitivity of Numerical Solutions to Time Step in a Nonlinear Atmospheric Model (비선형 대기 모형에서 수치 해의 시간 간격 민감도)

  • Lee, Hyunho;Baik, Jong-Jin;Han, Ji-Young
    • Journal of the Korean earth science society
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    • v.34 no.1
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    • pp.51-58
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    • 2013
  • An appropriate determination of time step is one of the important problems in atmospheric modeling. In this study, we investigate the sensitivity of numerical solutions to time step in a nonlinear atmospheric model. For this purpose, a simple nondimensional dynamical model is employed, and numerical experiments are performed with various time steps and nonlinearity factors. Results show that numerical solutions are not sensitive to time step when the nonlinearity factor is not influentially large and truncation error is negligible. On the other hand, when the nonlinearity factor is large (i.e., in a highly nonlinear regime), numerical solutions are found to be sensitive to time step. In this situation, smaller time step increases the intensity of the spatial filter, which makes small-scale phenomena weaken. This conflicts with the fact that smaller time step generally results in more accurate numerical solutions owing to reduced truncation error. This conflict is inevitable because the spatial filter is necessary to stabilize the numerical solutions of the nonlinear model.

The Solution of Mild-Slope Equation using Power Series (멱급수를 이용한 완경사 방정식의 해)

  • Jung, Tae-Hwa;Lee, Seung-Oh;Park, Jin-Ho;Cho, Yong-Sik
    • Journal of Korean Society of Hazard Mitigation
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    • v.8 no.1
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    • pp.133-138
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    • 2008
  • To analyze incident waves traveling from the deep ocean is very important in that it is based on resolving problems occurred in coastal areas. In general, numerical models and analytical solutions are used to analyze wave transformation. Although a numerical model can be applied to various bottoms and wave conditions, it may have some cumbersome numerical errors. On the other hand, an analytical solution has an advantage of obtaining the solution quickly and accurately without numerical errors. The analytical solution can, however, be utilized only for specific conditions. In this study, the analytical solution of the mild-slope equation has been developed. It can be applied to various conditions combing a numerical technique and an analytical approach while minimizing the numerical errors. As a result of comparing the obtained solutions in this study with those of the previously developed numerical model, A good agreement was observed.